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# Project M3: Level 3: Awesome Algebra: Looking for Patterns and Generalizations Student Mathematician's Journal

**Author(s):** *
Linda Jensen Sheffield, Suzanne H Chapin, Judith Dailey, Katherine Gavin *

** Edition: **
1

** Copyright: ** 2015

** Pages: ** 98

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Awesome Algebra: Looking for Patterns and GeneralizationsWe do not usually think of algebra as a topic for the elementary mathematics classroom. However, algebra is one of the five major content strands outlined by the National Council of Teachers of Mathematics (NCTM) in Principles and Standards for School Mathematics (2000). Looking for patterns, extending a pattern, making a generalization about a pattern -- all are part of algebraic thinking. So we talk about algebraic thinking or reasoning as opposed to the formal study of algebra. In our Project M³ unit Awesome Algebra: Looking for Patterns and Generalizations, students are encouraged to study patterns and determine how they change, how they can be extended or repeated and/or how they grow. They then move beyond this to organize the information systematically and analyze it to develop generalizations about the mathematical relationships in the patterns. There is a strong focus on mathematical discourse revolving around how to verbalize a generalization. During Awesome Algebra: Looking for Patterns and Generalizations students will be encouraged to use the idea of a variable as they think about how to represent a rule. This will help them become aware of the usefulness of a variable when representing a generalization. Our emphasis on number patterns is designed to challenge mathematically talented students by encouraging them to take a new look at basic number concepts, that is, arithmetic from an algebraic perspective. Students will become better estimators and give have effective tools to perform computation mentally. We hope that the experiences and discussions in the unit will provide a rich context for introducing students to algebraic thinking and strengthen their reasoning and communication skills. Student Mathematician's Journal The Student Mathematician's Journal is a unique feature of every unit in the Project M³ : Mentoring Mathematical Minds series, encouraging students to communicate in writing. It includes the student worksheets from each lesson. In these journals we ask students to reflect on what they have learned and write about it; in effect, they are working and acting like real mathematicians when they do this. Components used to teach this module:Awesome Algebra Teacher Guide (0-7575-2331-5)Awesome Algebra Student Mathematician's Journal

Awesome Algebra: Looking for Patterns and GeneralizationsWe do not usually think of algebra as a topic for the elementary mathematics classroom. However, algebra is one of the five major content strands outlined by the National Council of Teachers of Mathematics (NCTM) in Principles and Standards for School Mathematics (2000). Looking for patterns, extending a pattern, making a generalization about a pattern -- all are part of algebraic thinking. So we talk about algebraic thinking or reasoning as opposed to the formal study of algebra. In our Project M³ unit Awesome Algebra: Looking for Patterns and Generalizations, students are encouraged to study patterns and determine how they change, how they can be extended or repeated and/or how they grow. They then move beyond this to organize the information systematically and analyze it to develop generalizations about the mathematical relationships in the patterns. There is a strong focus on mathematical discourse revolving around how to verbalize a generalization. During Awesome Algebra: Looking for Patterns and Generalizations students will be encouraged to use the idea of a variable as they think about how to represent a rule. This will help them become aware of the usefulness of a variable when representing a generalization. Our emphasis on number patterns is designed to challenge mathematically talented students by encouraging them to take a new look at basic number concepts, that is, arithmetic from an algebraic perspective. Students will become better estimators and give have effective tools to perform computation mentally. We hope that the experiences and discussions in the unit will provide a rich context for introducing students to algebraic thinking and strengthen their reasoning and communication skills. Student Mathematician's Journal The Student Mathematician's Journal is a unique feature of every unit in the Project M³ : Mentoring Mathematical Minds series, encouraging students to communicate in writing. It includes the student worksheets from each lesson. In these journals we ask students to reflect on what they have learned and write about it; in effect, they are working and acting like real mathematicians when they do this. Components used to teach this module:Awesome Algebra Teacher Guide (0-7575-2331-5)Awesome Algebra Student Mathematician's Journal

Linda Jensen Sheffield

Linda Sheffield, Regents Professor Emerita of Mathematics Education at Northern Kentucky University, is a co-author of Math Innovations, a middle grades mathematics series as well as the Javits-funded *Project M ^{3}: Mentoring Mathematical Minds* and the NSF

*Project M*, two series of units for elementary and primary students. She a leader of the National Association for Gifted Children STEM Network, the National Council of Supervisors of Mathematics Special Interest Group on Mathematically Promising, was chair of the NCTM Task Force on Promising Students, and is past president of the School Science and Mathematics Association. Among the over 50 books that she has authored, co-authored, or edited are the NAGC/NCTM/NCSM monograph,

^{2}: Mentoring Young Mathematicians*Using the Common Core State Standards for Mathematics with Gifted and Advanced Learners*;

*The Peak in the Middle: Developing Mathematically Gifted Students in the Middle Grades*;

*Extending the Challenge in Mathematics*;

*Awesome Math Problems for Creative Thinking*; the PreK–2 NCTM

*Navigations*series; and math methods books for early childhood elementary and middle school teachers. She directed more than 20 state and national grants and has conducted seminars for educators, parents and students across the United States and in nearly twenty other countries with an emphasis on helping all students develop their mathematical creativity, promise, talents and abilities to the fullest extent possible.

Suzanne H Chapin

Suzanne H. Chapin, Ed.D. is an associate professor of mathematics education at Boston University, with expertise in mathematical discourse. She is also co-author of the *Project M³* units, an author for the NCTM *Navigations* Series in grades 3-5, and senior author of *Math Matters: Understanding the Math You Teach*, Grades K-6.

Judith Dailey

Judy is a retired teacher with 28 years of classroom experience and has served as Teacher in Residence for the Connecticut State Department of Education. She was the school district mathematics coordinator for grades K-8. She has co-authored NCTM’s Navigations in Geometry and Navigations in Measurement Grades 3-5 as well as Project M3 Measurement Grades 3-5 series. Judy is also the founder and chairperson for the Connecticut Association for Mathematically Precocious Youth.

Katherine Gavin

Dr. Katherine Gavin has over 30 years of experience in education as a mathematics teacher, math district coordinator, elementary assistant principal, and associate professor at the Neag Center for Gifted Education and Talent Development at the University of Connecticut. She is the Director and Senior Author of two multi-year curriculum research projects that involve the development of advanced mathematics units for mathematically talented students in Grades K-6. Research results show statistically significant mathematical achievement gains for the students in the projects over a comparison group of like-ability students. Project M3 units developed under a U.S. Department of Education research grant have won the National Association for Gifted Education (NAGC) Curriculum Division Award for six consecutive years. Dr. Gavin and her colleagues also received the 2009 Research Paper of the Year award from Gifted Child Quarterly, the leading United States research journal in gifted education, for an article that reported the Project M3 research results. Dr. Gavin is also the Director and Senior Author of the National Science Foundation Project M2, Mentoring Young Mathematicians, curriculum units for students in Kindergarten through Grade 2. Results again show statistically significant achievement gains for project students over the comparison group of students. This Project has received the NAGC Curriculum Division award for three consecutive years. She is also a co-author on the middle school mathematics textbook series, Math Innovations. Dr. Gavin’s awards include the 2006 Early Leader Award from NAGC, the 2012 Distinguished Researcher Award from the University of Connecticut, and the 2015 Robert A. Rosenbaum Leadership in Mathematics Award from the Association of Teachers of Mathematics in Connecticut (ATOMIC). Dr. Gavin has written over 100 articles and book chapters on gifted mathematics education, is a member of the writing team for the National Council of Teachers of Mathematics Navigations series and has co-authored a series of creative problem solving books. In addition, as a consultant she provides professional development for teachers and administrators in school districts throughout the United States and presents annually at national and international conferences including invited keynote presentations. For further information regarding her research projects and curriculum, please visit www.projectm3.org and www.projectm2.org.